1. Field of the Invention
The present invention relates generally to timing acquisition in a data stream. More particularly, the invention is directed to a method and apparatus for estimating the phase and the frequency for timing acquisition of a data stream.
2. Description of the Related Art
In electronic communications systems, during signal transmission, transmitted signals may be subject to noise. The received signal will be a combination of the original signal and the noise. The received signal data may be represented as the sum of the original signal and a noise component as follows:x=f(t)+n(t)   EQ 1where: f(t) is the original signal, and n(t) is noise.
The electronic communications system must be able to extract the information contained in the transmitted signal, even in the presence of noise.
In communications channels, data often is preceded by a preamble which has a fixed length of a known bit sequence. Sampling the preamble provides timing characteristics of the communications channel to enable receipt of the digital data.
The sampled preamble, X, may be represented by the following: X=[xO . . . xN]  EQ 2where
                              x          k                =                              A            ⁢                                                  ⁢                          sin              ⁡                              (                                  Φ                  +                                      k                    ·                    f                    ·                                          π                      2                                                                      )                                              +                      n            k                                              EQ        ⁢                                  ⁢        3                            A is the signal amplitude,        k is a sample point,        Φ is the phase of the data signal,        f is the frequency, and        nk is channel noise.        
The sampled preamble is then estimated, resulting in the following approximation, Y being the estimated preamble: Y=[yO . . . yN]  EQ 4where
                              y          k                =                              A            ^                    ⁢                      sin            ⁡                          (                                                Φ                  ^                                +                                  k                  ·                                      f                    ^                                    ·                                      π                    2                                                              )                                                          EQ        ⁢                                  ⁢        5                            Â is an estimated signal amplitude,        {circumflex over (Φ)} is an estimated phase, and        {circumflex over (f)} is an estimated frequency.        
Data may be transmitted reliably over the data channel when, after processing the preamble samples, the phase estimate is within 1% of the actual phase, and the frequency estimate is within 0.1%, preferably within 0.05% of the actual frequency. Traditionally, in the presence of a large frequency offset (a difference between the frequency estimate and the actual frequency), a preamble of sufficient length is required in order to have good frequency acquisition before the channel switches into the data mode. Often it is necessary to engage in a trade-off between timing loop bandwidth and the preamble length regarding the frequency acquisition. However there is a limit to such a compromise. For example, stability is a problem when the bandwidth is too large, especially when the timing loop delay cannot be ignored. Also, large bandwidth admits more noise, causing large jitters in the timing loop.
To improve the format efficiency of the digital data, it is desirable to have the preamble be as short as possible.